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<div class="title">bfgs.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef PCL_FOR_EIGEN_BFGS_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define PCL_FOR_EIGEN_BFGS_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160; </div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#if defined __GNUC__</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#  pragma GCC system_header </span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160; </div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &lt;pcl/registration/eigen.h&gt;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="keyword">namespace </span>Eigen</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;{</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;  <span class="keyword">template</span>&lt; <span class="keyword">typename</span> _Scalar &gt;</div>
<div class="line"><a name="l00013"></a><span class="lineno"><a class="line" href="class_eigen_1_1_polynomial_solver_3_01___scalar_00_012_01_4.html">   13</a></span>&#160;  <span class="keyword">class </span>PolynomialSolver&lt;_Scalar,2&gt; : <span class="keyword">public</span> PolynomialSolverBase&lt;_Scalar,2&gt;</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;  {</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <span class="keyword">public</span>:</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;      <span class="keyword">typedef</span> PolynomialSolverBase&lt;_Scalar,2&gt;    PS_Base;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;      EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keyword">public</span>:</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;      <span class="keyword">virtual</span> ~PolynomialSolver () {}</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;      <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;      <span class="keyword">inline</span> PolynomialSolver( <span class="keyword">const</span> OtherPolynomial&amp; poly, <span class="keywordtype">bool</span>&amp; hasRealRoot )</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;      {</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        compute( poly, hasRealRoot );</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;      }</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;      </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;      <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="class_eigen_1_1_polynomial_solver_3_01___scalar_00_012_01_4.html#a7c5ae6f9542326a694813d966d4f5ecb">   31</a></span>&#160;      <span class="keywordtype">void</span> <a class="code" href="class_eigen_1_1_polynomial_solver_3_01___scalar_00_012_01_4.html#a7c5ae6f9542326a694813d966d4f5ecb">compute</a>( <span class="keyword">const</span> OtherPolynomial&amp; poly, <span class="keywordtype">bool</span>&amp; hasRealRoot)</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;      {</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <span class="keyword">const</span> Scalar ZERO(0);</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        Scalar a2(2 * poly[2]);</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        assert( ZERO != poly[poly.size()-1] );</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        Scalar discriminant ((poly[1] * poly[1]) - (4 * poly[0] * poly[2]));</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        <span class="keywordflow">if</span> (ZERO &lt; discriminant)</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;          Scalar discriminant_root (std::sqrt (discriminant));</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;          m_roots[0] = (-poly[1] - discriminant_root) / (a2) ;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;          m_roots[1] = (-poly[1] + discriminant_root) / (a2) ;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;          hasRealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        }</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;          <span class="keywordflow">if</span> (ZERO == discriminant)</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;          {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            m_roots.resize (1);</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            m_roots[0] = -poly[1] / a2;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;            hasRealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;          }</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;          <span class="keywordflow">else</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;          {</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;            Scalar discriminant_root (std::sqrt (-discriminant));</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            m_roots[0] = RootType (-poly[1] / a2, -discriminant_root / a2);</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            m_roots[1] = RootType (-poly[1] / a2,  discriminant_root / a2);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;            hasRealRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;          }</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;      }</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;      </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;      <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;      <span class="keywordtype">void</span> compute( <span class="keyword">const</span> OtherPolynomial&amp; poly)</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      {</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordtype">bool</span> hasRealRoot;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        compute(poly, hasRealRoot);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;      }</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      <span class="keyword">using</span>                   PS_Base::m_roots;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  };</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;}</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> NX=Eigen::Dynamic&gt;</div>
<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="struct_b_f_g_s_dummy_functor.html">   74</a></span>&#160;<span class="keyword">struct </span><a class="code" href="struct_b_f_g_s_dummy_functor.html">BFGSDummyFunctor</a></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;{</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  <span class="keyword">typedef</span> _Scalar Scalar;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keyword">enum</span> { InputsAtCompileTime = NX };</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar,InputsAtCompileTime,1&gt; VectorType;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> m_inputs;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <a class="code" href="struct_b_f_g_s_dummy_functor.html">BFGSDummyFunctor</a>() : m_inputs(InputsAtCompileTime) {}</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <a class="code" href="struct_b_f_g_s_dummy_functor.html">BFGSDummyFunctor</a>(<span class="keywordtype">int</span> inputs) : m_inputs(inputs) {}</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  <span class="keyword">virtual</span> ~<a class="code" href="struct_b_f_g_s_dummy_functor.html">BFGSDummyFunctor</a>() {}</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <span class="keywordtype">int</span> inputs()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_inputs; }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <span class="keyword">virtual</span> <span class="keywordtype">double</span> operator() (<span class="keyword">const</span> VectorType &amp;x) = 0;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <span class="keyword">virtual</span> <span class="keywordtype">void</span>  df(<span class="keyword">const</span> VectorType &amp;x, VectorType &amp;df) = 0;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="keyword">virtual</span> <span class="keywordtype">void</span> fdf(<span class="keyword">const</span> VectorType &amp;x, Scalar &amp;f, VectorType &amp;df) = 0;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;};</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;<span class="keyword">namespace </span>BFGSSpace {</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="keyword">enum</span> Status {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    NegativeGradientEpsilon = -3,</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    NotStarted = -2,</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    Running = -1,</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    Success = 0,</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    NoProgress = 1</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  };</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;}</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt;</div>
<div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="class_b_f_g_s.html">  114</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_b_f_g_s.html">BFGS</a></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;{</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> FunctorType::Scalar Scalar;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> FunctorType::VectorType FVectorType;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <a class="code" href="class_b_f_g_s.html">BFGS</a>(FunctorType &amp;_functor) </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;      : pnorm(0), g0norm(0), iter(-1), functor(_functor) {  }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <span class="keyword">typedef</span> Eigen::DenseIndex Index;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="struct_b_f_g_s_1_1_parameters.html">  125</a></span>&#160;  <span class="keyword">struct </span><a class="code" href="struct_b_f_g_s_1_1_parameters.html">Parameters</a> {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <a class="code" href="struct_b_f_g_s_1_1_parameters.html">Parameters</a>()</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    : max_iters(400)</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;      , bracket_iters(100)</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;      , section_iters(100)</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;      , rho(0.01)</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;      , sigma(0.01)</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      , tau1(9)</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      , tau2(0.05)</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;      , tau3(0.5)</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      , step_size(1)</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      , order(3) {}</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    Index max_iters;   <span class="comment">// maximum number of function evaluation</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    Index bracket_iters;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    Index section_iters;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    Scalar rho;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    Scalar sigma;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    Scalar tau1;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    Scalar tau2;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    Scalar tau3;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    Scalar step_size;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    Index order;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  };</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  BFGSSpace::Status minimize(FVectorType &amp;x);</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  BFGSSpace::Status minimizeInit(FVectorType &amp;x);</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  BFGSSpace::Status minimizeOneStep(FVectorType &amp;x);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  BFGSSpace::Status testGradient(Scalar epsilon);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="keywordtype">void</span> resetParameters(<span class="keywordtype">void</span>) { parameters = <a class="code" href="struct_b_f_g_s_1_1_parameters.html">Parameters</a>(); }</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  </div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  Parameters parameters;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  Scalar f;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  FVectorType gradient;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  </div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <a class="code" href="class_b_f_g_s.html">BFGS</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="class_b_f_g_s.html">BFGS</a>&amp;);</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  BFGSSpace::Status lineSearch (Scalar rho, Scalar sigma, </div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                                Scalar tau1, Scalar tau2, Scalar tau3,</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                                <span class="keywordtype">int</span> order, Scalar alpha1, Scalar &amp;alpha_new);</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  Scalar interpolate (Scalar a, Scalar fa, Scalar fpa,</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                      Scalar b, Scalar fb, Scalar fpb, Scalar xmin, Scalar xmax,</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                      <span class="keywordtype">int</span> order);  </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keywordtype">void</span> checkExtremum (<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, 4, 1&gt;&amp; coefficients, Scalar x, Scalar&amp; xmin, Scalar&amp; fmin);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keywordtype">void</span> moveTo (Scalar alpha);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  Scalar slope ();</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  Scalar applyF (Scalar alpha);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  Scalar applyDF (Scalar alpha);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <span class="keywordtype">void</span> applyFDF (Scalar alpha, Scalar &amp;f, Scalar &amp;df);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  <span class="keywordtype">void</span> updatePosition (Scalar alpha, FVectorType&amp; x, Scalar&amp; f, FVectorType&amp; g);</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="keywordtype">void</span> changeDirection ();</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  Scalar delta_f, fp0;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  FVectorType x0, dx0, dg0, g0, dx, p;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  Scalar pnorm, g0norm;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160; </div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  Scalar f_alpha;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  Scalar df_alpha;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  FVectorType x_alpha;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  FVectorType g_alpha;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  </div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  <span class="comment">// cache &quot;keys&quot;</span></div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  Scalar f_cache_key;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  Scalar df_cache_key;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  Scalar x_cache_key;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  Scalar g_cache_key;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160; </div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  Index iter;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  FunctorType &amp;functor;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;};</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::checkExtremum</a>(<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, 4, 1&gt;&amp; coefficients, Scalar x, Scalar&amp; xmin, Scalar&amp; fmin)</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;{</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  Scalar y = Eigen::poly_eval(coefficients, x);</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordflow">if</span>(y &lt; fmin) { xmin = x; fmin = y; }</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;}</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::moveTo</a>(Scalar alpha)</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;{</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  x_alpha = x0 + alpha * p;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  x_cache_key = alpha;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;}</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160; </div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keyword">typename</span> BFGS&lt;FunctorType&gt;::Scalar</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::slope</a>()</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;{</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keywordflow">return</span> (g_alpha.dot (p));</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;}</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160; </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keyword">typename</span> BFGS&lt;FunctorType&gt;::Scalar</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::applyF</a>(Scalar alpha)</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;{</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  <span class="keywordflow">if</span> (alpha == f_cache_key) <span class="keywordflow">return</span> f_alpha;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  moveTo (alpha);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  f_alpha = functor (x_alpha);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  f_cache_key = alpha;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="keywordflow">return</span> (f_alpha);</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;}</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keyword">typename</span> BFGS&lt;FunctorType&gt;::Scalar</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::applyDF</a>(Scalar alpha)</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;{</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">if</span> (alpha == df_cache_key) <span class="keywordflow">return</span> df_alpha;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  moveTo (alpha);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  <span class="keywordflow">if</span>(alpha != g_cache_key)</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  {</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    functor.df (x_alpha, g_alpha);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    g_cache_key = alpha;</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  }</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  df_alpha = slope ();</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  df_cache_key = alpha;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keywordflow">return</span> (df_alpha);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;}</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::applyFDF</a>(Scalar alpha, Scalar&amp; f, Scalar&amp; df)</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;{</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keywordflow">if</span>(alpha == f_cache_key &amp;&amp; alpha == df_cache_key)</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  {</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    f = f_alpha;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    df = df_alpha;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  }</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160; </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <span class="keywordflow">if</span>(alpha == f_cache_key || alpha == df_cache_key)</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  {</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    f = applyF (alpha);</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    df = applyDF (alpha);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  }</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  moveTo (alpha);</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  functor.fdf (x_alpha, f_alpha, g_alpha);</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  f_cache_key = alpha;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  g_cache_key = alpha;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  df_alpha = slope ();</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  df_cache_key = alpha;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  f = f_alpha;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  df = df_alpha;</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;}</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::updatePosition</a> (Scalar alpha, FVectorType &amp;x, Scalar &amp;f, FVectorType &amp;g)</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;{</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  { </div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    Scalar f_alpha, df_alpha; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    applyFDF (alpha, f_alpha, df_alpha); </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  } ;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  f = f_alpha;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;  x = x_alpha;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  g = g_alpha;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;}  </div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160; </div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::changeDirection</a> ()</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;{</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  x_alpha = x0;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  x_cache_key = 0.0;</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  f_cache_key = 0.0;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  g_alpha = g0;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  g_cache_key = 0.0;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  df_alpha = slope ();</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  df_cache_key = 0.0;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;}</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160; </div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; BFGSSpace::Status</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::minimize</a>(FVectorType  &amp;x)</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;{</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  BFGSSpace::Status status = minimizeInit(x);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    status = minimizeOneStep(x);</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    iter++;</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  } <span class="keywordflow">while</span> (status==BFGSSpace::Success &amp;&amp; iter &lt; parameters.max_iters);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="keywordflow">return</span> status;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;}</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160; </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; BFGSSpace::Status</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::minimizeInit</a>(FVectorType  &amp;x)</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;{</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  iter = 0;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  delta_f = 0;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  dx.setZero ();</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  functor.fdf(x, f, gradient);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  x0 = x;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  g0 = gradient;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  g0norm = g0.norm ();</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  p = gradient * -1/g0norm;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  pnorm = p.norm ();</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  fp0 = -g0norm;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160; </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  {</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    x_alpha = x0; x_cache_key = 0;</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    f_alpha = f; f_cache_key = 0;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    </div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    g_alpha = g0; g_cache_key = 0;</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    </div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    df_alpha = slope (); df_cache_key = 0;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  }</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160; </div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keywordflow">return</span> BFGSSpace::NotStarted;</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;}</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160; </div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; BFGSSpace::Status</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::minimizeOneStep</a>(FVectorType  &amp;x)</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;{</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  Scalar alpha = 0.0, alpha1;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  Scalar f0 = f;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  <span class="keywordflow">if</span> (pnorm == 0.0 || g0norm == 0.0 || fp0 == 0)</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  {</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;    dx.setZero ();</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    <span class="keywordflow">return</span> BFGSSpace::NoProgress;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  }</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160; </div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  <span class="keywordflow">if</span> (delta_f &lt; 0)</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  {</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;    Scalar del = std::max (-delta_f, 10 * std::numeric_limits&lt;Scalar&gt;::epsilon() * fabs(f0));</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    alpha1 = std::min (1.0, 2.0 * del / (-fp0));</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  }</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    alpha1 = fabs(parameters.step_size);</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160; </div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  BFGSSpace::Status status = lineSearch(parameters.rho, parameters.sigma, </div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;                                        parameters.tau1, parameters.tau2, parameters.tau3, </div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;                                        parameters.order, alpha1, alpha);</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160; </div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="keywordflow">if</span>(status != BFGSSpace::Success)</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;    <span class="keywordflow">return</span> status;</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160; </div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  updatePosition(alpha, x, f, gradient);</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160; </div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  delta_f = f - f0;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160; </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  <span class="comment">/* Choose a new direction for the next step */</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  {</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <span class="comment">/* This is the BFGS update: */</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="comment">/* p&#39; = g1 - A dx - B dg */</span></div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="comment">/* A = - (1+ dg.dg/dx.dg) B + dg.g/dx.dg */</span></div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <span class="comment">/* B = dx.g/dx.dg */</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160; </div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;    Scalar dxg, dgg, dxdg, dgnorm, A, B;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    <span class="comment">/* dx0 = x - x0 */</span></div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;    dx0 = x - x0;</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;    dx = dx0; <span class="comment">/* keep a copy */</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;    <span class="comment">/* dg0 = g - g0 */</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;    dg0 = gradient - g0;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;    dxg = dx0.dot (gradient);</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    dgg = dg0.dot (gradient);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;    dxdg = dx0.dot (dg0);</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    dgnorm = dg0.norm ();</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160; </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    <span class="keywordflow">if</span> (dxdg != 0)</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    {</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;      B = dxg / dxdg;</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;      A = -(1.0 + dgnorm * dgnorm / dxdg) * B + dgg / dxdg;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    }</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    {</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;      B = 0;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;      A = 0;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    }</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160; </div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    p = -A * dx0;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    p+= gradient;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    p+= -B * dg0 ;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  }</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160; </div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  g0 = gradient;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;  x0 = x;</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;  g0norm = g0.norm ();</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;  pnorm = p.norm ();</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;  </div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  Scalar dir = ((p.dot (gradient)) &gt; 0) ? -1.0 : 1.0;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  p*= dir / pnorm;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;  pnorm = p.norm ();</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  fp0 = p.dot (g0);</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  changeDirection();</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;  <span class="keywordflow">return</span> BFGSSpace::Success;</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;}</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160; </div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keyword">typename</span> BFGSSpace::Status </div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::testGradient</a>(Scalar epsilon)</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;{</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;  <span class="keywordflow">if</span>(epsilon &lt; 0)</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="keywordflow">return</span> BFGSSpace::NegativeGradientEpsilon;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  {</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keywordflow">if</span>(gradient.norm () &lt; epsilon)</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;      <span class="keywordflow">return</span> BFGSSpace::Success;</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;      <span class="keywordflow">return</span> BFGSSpace::Running;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  }</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;}</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160; </div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; <span class="keyword">typename</span> BFGS&lt;FunctorType&gt;::Scalar </div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::interpolate</a> (Scalar a, Scalar fa, Scalar fpa,</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;                                Scalar b, Scalar fb, Scalar fpb, </div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;                                Scalar xmin, Scalar xmax,</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;                                <span class="keywordtype">int</span> order)</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;{</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;  <span class="comment">/* Map [a,b] to [0,1] */</span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  Scalar y, alpha, ymin, ymax, fmin;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160; </div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;  ymin = (xmin - a) / (b - a);</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;  ymax = (xmax - a) / (b - a);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  </div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  <span class="comment">// Ensure ymin &lt;= ymax</span></div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  <span class="keywordflow">if</span> (ymin &gt; ymax) { Scalar tmp = ymin; ymin = ymax; ymax = tmp; };</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160; </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;  <span class="keywordflow">if</span> (order &gt; 2 &amp;&amp; !(fpb != fpa) &amp;&amp; fpb != std::numeric_limits&lt;Scalar&gt;::infinity ())</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  {</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    fpa = fpa * (b - a);</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    fpb = fpb * (b - a);</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160; </div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    Scalar eta = 3 * (fb - fa) - 2 * fpa - fpb;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    Scalar xi = fpa + fpb - 2 * (fb - fa);</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    Scalar c0 = fa, c1 = fpa, c2 = eta, c3 = xi;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    Scalar y0, y1;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    Eigen::Matrix&lt;Scalar, 4, 1&gt; coefficients;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    coefficients &lt;&lt; c0, c1, c2, c3;</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    </div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    y = ymin; </div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <span class="comment">// Evaluate the cubic polyinomial at ymin;</span></div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    fmin = Eigen::poly_eval (coefficients, ymin);</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    checkExtremum (coefficients, ymax, y, fmin);</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    {</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;      <span class="comment">// Solve quadratic polynomial for the derivate</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;      Eigen::Matrix&lt;Scalar, 3, 1&gt; coefficients2;</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;      coefficients2 &lt;&lt; c1, 2 * c2, 3 * c3;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      <span class="keywordtype">bool</span> real_roots;</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      Eigen::PolynomialSolver&lt;Scalar, 2&gt; solver (coefficients2, real_roots);</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;      <span class="keywordflow">if</span>(real_roots)</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;      {</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;        <span class="keywordflow">if</span> ((solver.roots ()).size () == 2)  <span class="comment">/* found 2 roots */</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;        {</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;          y0 = std::real (solver.roots () [0]);</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;          y1 = std::real (solver.roots () [1]);</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;          <span class="keywordflow">if</span>(y0 &gt; y1) { Scalar tmp (y0); y0 = y1; y1 = tmp; }</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;          <span class="keywordflow">if</span> (y0 &gt; ymin &amp;&amp; y0 &lt; ymax) </div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;            checkExtremum (coefficients, y0, y, fmin);</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;          <span class="keywordflow">if</span> (y1 &gt; ymin &amp;&amp; y1 &lt; ymax) </div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;            checkExtremum (coefficients, y1, y, fmin);</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;        }</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((solver.roots ()).size () == 1)  <span class="comment">/* found 1 root */</span></div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;        {</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;          y0 = std::real (solver.roots () [0]);</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;          <span class="keywordflow">if</span> (y0 &gt; ymin &amp;&amp; y0 &lt; ymax) </div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;            checkExtremum (coefficients, y0, y, fmin);</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;        }</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;      }</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    }</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;  } </div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;  {</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    fpa = fpa * (b - a);</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    Scalar fl = fa + ymin*(fpa + ymin*(fb - fa -fpa));</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;    Scalar fh = fa + ymax*(fpa + ymax*(fb - fa -fpa));</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    Scalar c = 2 * (fb - fa - fpa);       <span class="comment">/* curvature */</span></div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;    y = ymin; fmin = fl;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    </div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;    <span class="keywordflow">if</span> (fh &lt; fmin) { y = ymax; fmin = fh; } </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    </div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    <span class="keywordflow">if</span> (c &gt; a)  <span class="comment">/* positive curvature required for a minimum */</span></div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    {</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;      Scalar z = -fpa / c;      <span class="comment">/* location of minimum */</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;      <span class="keywordflow">if</span> (z &gt; ymin &amp;&amp; z &lt; ymax) {</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;        Scalar f = fa + z*(fpa + z*(fb - fa -fpa));</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;        <span class="keywordflow">if</span> (f &lt; fmin) { y = z; fmin = f; };</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;      }</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;    }</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  }</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  </div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  alpha = a + y * (b - a);</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  <span class="keywordflow">return</span> alpha;</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;}</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160; </div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt; BFGSSpace::Status </div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;<a class="code" href="class_b_f_g_s.html">BFGS&lt;FunctorType&gt;::lineSearch</a>(Scalar rho, Scalar sigma, </div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;                              Scalar tau1, Scalar tau2, Scalar tau3,</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;                              <span class="keywordtype">int</span> order, Scalar alpha1, Scalar &amp;alpha_new)</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;{</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  Scalar f0, fp0, falpha, falpha_prev, fpalpha, fpalpha_prev, delta, alpha_next;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  Scalar alpha = alpha1, alpha_prev = 0.0;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  Scalar a, b, fa, fb, fpa, fpb;</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  Index i = 0;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160; </div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  applyFDF (0.0, f0, fp0);</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160; </div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  falpha_prev = f0;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  fpalpha_prev = fp0;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160; </div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;  <span class="comment">/* Avoid uninitialized variables morning */</span></div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  a = 0.0; b = alpha;</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  fa = f0; fb = 0.0;</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  fpa = fp0; fpb = 0.0;</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160; </div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;  <span class="comment">/* Begin bracketing */</span>  </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160; </div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;  <span class="keywordflow">while</span> (i++ &lt; parameters.bracket_iters)</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;  {</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    falpha = applyF (alpha);</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160; </div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    <span class="keywordflow">if</span> (falpha &gt; f0 + alpha * rho * fp0 || falpha &gt;= falpha_prev)</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;    {</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;      a = alpha_prev; fa = falpha_prev; fpa = fpalpha_prev;</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;      b = alpha; fb = falpha; fpb = std::numeric_limits&lt;Scalar&gt;::quiet_NaN ();</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    } </div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160; </div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;    fpalpha = applyDF (alpha);</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160; </div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    <span class="comment">/* Fletcher&#39;s sigma test */</span></div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    <span class="keywordflow">if</span> (fabs (fpalpha) &lt;= -sigma * fp0)</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    {</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;      alpha_new = alpha;</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;      <span class="keywordflow">return</span> BFGSSpace::Success;</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    }</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160; </div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <span class="keywordflow">if</span> (fpalpha &gt;= 0)</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;    {</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;      a = alpha; fa = falpha; fpa = fpalpha;</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;      b = alpha_prev; fb = falpha_prev; fpb = fpalpha_prev;</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;      <span class="keywordflow">break</span>;                <span class="comment">/* goto sectioning */</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;    }</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160; </div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;    delta = alpha - alpha_prev;</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160; </div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;    {</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;      Scalar lower = alpha + delta;</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;      Scalar upper = alpha + tau1 * delta;</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160; </div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;      alpha_next = interpolate (alpha_prev, falpha_prev, fpalpha_prev,</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;                                alpha, falpha, fpalpha, lower, upper, order);</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160; </div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;    }</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160; </div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    alpha_prev = alpha;</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;    falpha_prev = falpha;</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;    fpalpha_prev = fpalpha;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    alpha = alpha_next;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  }</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;  <span class="comment">/*  Sectioning of bracket [a,b] */</span></div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="keywordflow">while</span> (i++ &lt; parameters.section_iters)</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  {</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    delta = b - a;</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;      </div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;    {</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;      Scalar lower = a + tau2 * delta;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;      Scalar upper = b - tau3 * delta;</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;        </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;      alpha = interpolate (a, fa, fpa, b, fb, fpb, lower, upper, order);</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;    }</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;    falpha = applyF (alpha);</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;    <span class="keywordflow">if</span> ((a-alpha)*fpa &lt;= std::numeric_limits&lt;Scalar&gt;::epsilon ()) {</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;      <span class="comment">/* roundoff prevents progress */</span></div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;      <span class="keywordflow">return</span> BFGSSpace::NoProgress;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;    };</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160; </div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;    <span class="keywordflow">if</span> (falpha &gt; f0 + rho * alpha * fp0 || falpha &gt;= fa)</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;    {</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;      <span class="comment">/*  a_next = a; */</span></div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;      b = alpha; fb = falpha; fpb = std::numeric_limits&lt;Scalar&gt;::quiet_NaN ();</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;    }</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;    {</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;      fpalpha = applyDF (alpha);</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;          </div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;      <span class="keywordflow">if</span> (fabs(fpalpha) &lt;= -sigma * fp0)</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;      {</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;        alpha_new = alpha;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;        <span class="keywordflow">return</span> BFGSSpace::Success;  <span class="comment">/* terminate */</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;      }</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;          </div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;      <span class="keywordflow">if</span> ( ((b-a) &gt;= 0 &amp;&amp; fpalpha &gt;= 0) || ((b-a) &lt;=0 &amp;&amp; fpalpha &lt;= 0))</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;      {</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;        b = a; fb = fa; fpb = fpa;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;        a = alpha; fa = falpha; fpa = fpalpha;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;      }</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;      {</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;        a = alpha; fa = falpha; fpa = fpalpha;</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;      }</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;    }</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;  }</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  <span class="keywordflow">return</span> BFGSSpace::Success;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;}</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// PCL_FOR_EIGEN_BFGS_H</span></div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160; </div>
<div class="ttc" id="aclass_b_f_g_s_html"><div class="ttname"><a href="class_b_f_g_s.html">BFGS</a></div><div class="ttdef"><b>Definition:</b> bfgs.h:115</div></div>
<div class="ttc" id="aclass_eigen_1_1_polynomial_solver_3_01___scalar_00_012_01_4_html_a7c5ae6f9542326a694813d966d4f5ecb"><div class="ttname"><a href="class_eigen_1_1_polynomial_solver_3_01___scalar_00_012_01_4.html#a7c5ae6f9542326a694813d966d4f5ecb">Eigen::PolynomialSolver&lt; _Scalar, 2 &gt;::compute</a></div><div class="ttdeci">void compute(const OtherPolynomial &amp;poly, bool &amp;hasRealRoot)</div><div class="ttdef"><b>Definition:</b> bfgs.h:31</div></div>
<div class="ttc" id="astruct_b_f_g_s_1_1_parameters_html"><div class="ttname"><a href="struct_b_f_g_s_1_1_parameters.html">BFGS::Parameters</a></div><div class="ttdef"><b>Definition:</b> bfgs.h:125</div></div>
<div class="ttc" id="astruct_b_f_g_s_dummy_functor_html"><div class="ttname"><a href="struct_b_f_g_s_dummy_functor.html">BFGSDummyFunctor</a></div><div class="ttdef"><b>Definition:</b> bfgs.h:75</div></div>
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